Positive solutions for a nonconvex elliptic Dirichlet problem with superlinear response

The existence of bounded solutions of the Dirichlet problem for a ceratin class of elliptic partial differential equations is discussed here. We use variational methods based on the subdifferential theory and the comparison principle for difergence form operators. We present duality and variational principles for this problem. As a consequences of the duality we obtain also the variational principle for minimizing sequences of J which gives a measure of a duality gap between primal and dual functional for approximate solutions.